This talk will present an updated and simplified version of the proof of EnKF
convergence in the gaussian case from Mandel, Cobb, and Beezley
http://dx.doi.org/10.1007/s10492-011-0031-2 . The proof relies on the fact that
the ensemble is a finite exchangeable sequence of random elements.
Generalizations and obstacles to a generalization will be discussed. While all
seems to be good for an ensemble in a Hilbert space with finite dimensional
data, extension to the case of infinitely dimensional data runs into a
difficulty when the data perturbation is white noise. Square root ensemble
filters do not involve a data perturbation, but the generated ensemble may not
be exchangeable, except for the ensemble adjustment Kalman filter (EAKF), which
does make exchangeable ensembles.